任意长度W变换的统一算法及其实现

任意长度Ｗ变换的统一算法及其实现曾泳泓,蒋增荣（国防科技大学）ＡＵＮＩＦＩＥＤＭＳＴＡＬＧＯＲＩＴＨＭＦＯＲＴＨＥＤＩＳＣＲＥＴＥＷＴＲＡＮＳＦＯＲＭＷＩＴＨＡＲＢＩＴＲＡＲＶＬＥＮＧＴＨ￥ＺｅｎｇＹｏｎｇ－ｈｏｎｇ;ＪｉａｎｇＺｅｎｇ－ｒｏｎｇ（７...     

离散卷积的W变换算法

离散卷积的Ｗ变换算法曾泳泓（国防科技大学）ＣＯＭＰＵＴＩＮＧＤＩＳＣＲＥＴＥＣＯＮＶＯＬＵＴＩＯＮＳＢＹＷＴＲＡＮＳＦＯＲＭ￥ＺｅｎｇＹｏｎｇ－ｈｏｎｇ（ＮａｔｉｏｎａｌＵｎｉｖｅｒｓｉｔｙＯｆＤｅｆｅｎｓｅＴｅｃｈｎｏｌｏｇｙ）Ａｂｓｔｒａｃｔ：Ｆ...     

任意长度离散余弦变换的快速算法

§1.引言 离散余弦变换(DCT)有趋于统计最佳交换Kavhunven-Lave变换(KLT)的渐近性质,在通信和信号处理中应用广泛,并在许多方面比离散富里叶变换(DFT)更好。     

离散积分小波变换的快速算法

本文讨论了积分小波变换的快速算法,通过尺度函数与小波间的二尺度关系,导出了一个实现积分小波变换的快速计算方法及相应滤波器的构造方法。     

离散Ter变换的快速算法

本文研究了第 ( 2 ,0 )类离散 Walsh-Haar类变换即离散 Ter变换的快速算法 .     

离散余弦变换的一种推广

离散余弦变换(DCT)在数字信号、图像处理、频谱分析、数据压缩和信息隐藏等领域有着广泛的应用.推广离散余弦变换,给出一个包含三个参数的统一表达式,并证明在许多情形新变换是正交变换.最后给出一种新型离散余弦变换,并证明它是正交变换.     

用离散Fourier变换求一类矩阵特征值

用离散Fourm变换求包括三对角差分矩阵法在内的一类矩阵的持征值以厦特征向量．     

用离散Fourier变换求一类矩阵特征值

用离散Fourier 变换求包括三对角差分矩阵法在内的一类矩阵的特征值以及特征向量.     

对称 Toeplitz 系统的快速W变换基预条件子

１．引言考虑下列Ｎ阶线性方程组其中T_N=(t_i,j)　是Ｎ×Ｎ阶实对称正定（ＳＰＤ）Ｔｏｅｐｌｉｔｚ矩阵,即０,１,…,Ｎ－１）且Ｔ_Ｎ的所有特征值为正数．Ｔｏｅｐｌｉｔｚ系统已广泛应用于数字信号处理,时间序列分析（参见［１］）以及微分方程的数值解（参见［２１］等领域．八十年代以前,考虑到Ｔｏｅｐｌｉｔｚ矩阵的特殊性,人们主要用Ｌｅｖｉｎｓｏｎ递推技术及其变形或者分而治之思想直接求解方程组（１．１）,计算复杂性为Ｏ（Ｎ~（２））或Ｏ（ＮｌｏｇＮ~（２））（参见［３］）;比Ｇａｕｓｓ法运算量级Ｏ（Ｎ~（３）…     

矩阵分解与Chrestenson谱的计算

本文研究离散Fourier变换的一类变型-整数模合数m剩余类环上n元函数的Chrestenson谱的快速计算,基于稀疏矩阵分解,给出了两种复杂度为O(mⁿn∑^r_i=1p_i)的计算Chrestenson谱的快速算法,其中p₁p₂…p_r是m的素因子分解.     

An Algorithm for Computing Fundamental Solutions of Difference Operators

We propose an FFT-based algorithm for computing fundamental solutions of difference operators with constant coefficients. Our main contribution is to handle cases where the symbol has zeros.     

Fast Wavelet Transform for Toeplitz Matrices and Property Analysis

Fast wavelet transform algorithms for Toeplitz matrices are proposed in this paper. Distinctive from the well known discrete trigonometric transforms, such as the discrete cosine transform （DCT） and the discrete Fourier transform （DFT） for Toeplitz matrices, the new algorithms are achieved by compactly supported wavelet that preserve the character of a Toeplitz matrix after transform, which is quite useful in many applications involving a Toeplitz matrix. Results of numerical experiments show that the proposed method has good compression performance similar to using wavelet in the digital image coding. Since the proposed algorithms turn a dense Toeplitz matrix into a band-limited form, the arithmetic operations required by the new algorithms are O（N） that are reduced greatly compared with O（N log N） by the classical trigonometric transforms.     

A fast spherical harmonics transform algorithm

The spectral method with discrete spherical harmonics transform plays an important role in many applications. In spite of its advantages, the spherical harmonics transform has a drawback of high computational complexity, which is determined by that of the associated Legendre transform, and the direct computation requires time of for cut-off frequency . In this paper, we propose a fast approximate algorithm for the associated Legendre transform. Our algorithm evaluates the transform by means of polynomial interpolation accelerated by the Fast Multipole Method (FMM). The divide-and-conquer approach with split Legendre functions gives computational complexity . Experimental results show that our algorithm is stable and is faster than the direct computation for .

     

两两序列比对的一种新方法

本文研究DNA的两两序列比时,提出了基于快速沃尔什变换的新方法。经过计算模拟分析可知,比对的时间复杂度和空间复杂度明显降低.     

斜Haar类变换的演化生成与快速算法

1.引 言 Haar函数和Walsh函数是两类密切相关且十分重要的完备正交函数系,它们不仅在(离散)正交变换及其快速算法设计中起着重要的作用,而且在小波分析中占有重要地位:它们分别对应于Haar小波和Haar小波包.另外,它们还是遗传算法和密码学等涉及布尔函数或离散函数的学科之重要的理论分析工具.